The word repentance triggers different meanings in the mind of Christians. The most common being regret for past actions and way of living your life prior to accepting Christ as your Savior. And this person would be correct.
However, repentance means way much more than that. The greek word for repentance is 'metanoia', meta= beyond and noia (nous)= mind, thought.
In 1 Corinthians 2:16, Saint Paul says that we have the mind of Christ. So, a repented person is a person who acquired the mind/thought of God. Why must a Christian repent/change his mind with God's mind? Because this is the only way you can do God's will. There is a close relation between the way you live your life and the way you think. Don't think like the world! Don't be of the world because our God is not of this world! The mind of God is comprised in the Gospel.
At the Terrifying Last Judgment each one will present the fruits of his faith to the Judge (Jesus Christ). Some people believe but don't bring fruits because their faith is dead, some people don't believe in God, they think this is a joke, a bednight story. Let's analyse ourselves and bring fruits worthy of repentance because our God is ALIVE and is NOT JOKING.
Yes, the Greek word for "repent" is "metanoia" (noun) and "matanoeo" (verb) you see as defined in the Strongs #3340, 3341:
to think differently or afterwards, reconsider. After thought, change of mind. Repentance basically means a "change of mind" and the context must determine what is involved in this change of mind. Where salvation is in view, repentance actually precedes saving faith in Christ and is not a totally separate act from faith. It is actually the same coin with two sides. Repentance is on one side (what you change your mind about) and faith in Christ is on the positive side, (the new direction of this change of mind). Repentance and faith are two sides of the same experience of receiving Christ.
In the context of Luke 13:3, Jesus challenged the people's notion that they were morally superior to those who suffered in such catastrophes. He called all to
repent or perish. For some people though, prior to coming to the end result of repentance in receiving salvation (faith in Christ), they must change their minds about other specific things in order to get there. Repentance, metanoia, focuses on changing one's mind about his previous concept of God (as in Acts 17:30) and disbelief in God or false beliefs (polytheism and idolatry) about God (1 Thessalonians 1:9). On the other hand, this change of mind, focuses on the new direction that change about God must ultimately take, namely, trusting in Jesus Christ as the ALL-sufficient means of our salvation.
The Bible also tells us that true repentance will
result in a change of actions. Acts 26:20 declares, "I preached that they should repent and turn to God and
prove their repentance by their deeds." This is the
fruit of repentance (Matthew 3:8) and not the essence of repentance (change of mind). Certain people confuse the "fruit of repentance" with the "essence of repentance" (and also do the same thing with faith) and end up teaching salvation by works. All genuine believers are fruitful, yet not all are equally fruitful. (Matthew 13:23) We are not saved by an empty profession of faith that demonstrates by the lack of works that it's dead. (James 2:14)